Question

two blocks a and b float in water if block a floats with 1/4 of its volume immersed and block b floats with 3/5 of volume immersed the ratio of density of block a to b is

Answer 1

The ratio of the density of block a to b is 5:12.

Explanation:

For block a:

Block a floats with ¼ of its total volume immersed i.e., Volume of the block “a” inside the water, Vaw = ¼ * total volume(Va)

We know that according to the Archimedes principle of floating,

[The weight of the body] = [Force of buoyancy]

⇒ [Va * ρa * g] = [Vw * ρw * g] …… [where ρa = density of block a and ρw = density of water]

⇒ [Va * ρa * g] = [(1/4 * Va) * ρw * g]

Cancelling the similar terms

⇒ ρa = ¼ * ρw …… (i)

For block b:

Block b floats with 3/5th of its total volume immersed i.e., Volume of the block “b” inside the water, Vbw = $\frac{3}{5}$ * total volume(Vb)

Again, according to the Archimedes principle,

[The weight of the body] = [Force of buoyancy]

⇒ [Vb * ρb * g] = [Vbw * ρw * g] …… [where ρb = density of block b]

⇒ [Vb * ρb * g] = [(3/5 * Vb) * ρw * g]

Cancelling the similar terms

⇒ ρb = $\frac{3}{5}$ * ρw …… (ii)

Thus, from (i) & (ii), we get

The ratio of the density of block a to block b as,

= ρa / ρb

= [¼ * ρw] / [$\frac{3}{5}$ * ρw]

= $\frac{5}{3*4}$

= $\frac{5}{12}$

---------------------------------------------------------------------------------------

Also View:

Two solids A and B float in water.It is observed that A floats with half of its volume immersed and B floats with 2/3 of its volume immersed.What is the ratio of their densities?

https://brainly.in/question/1032598